Motivic Adams E₂: cohomology of δ, products and Massey products - #290
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`multiply_with_allocation` branched on `generic()`, but the two arms were the same computation: `multiply_qpart(m1, 0)` returns `[(1, m1)]`, so the classical arm is the generic one with an empty exterior part. Collapse them into `milnor_product`, a free function that reports each `(coefficient, basis element)` through a callback, leaving the index lookup and excess filter to the caller. `multiply_qpart` becomes free too; it only ever read the prime. `generic` was a `bool` field written once as `p != 2` and never mutated. Derive it instead. That also drops its `#[cfg(feature = "odd-primes")]` gate: without the feature `ValidPrime` is the zero-sized type 2, so the comparison folds to a constant on its own. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F25ZVbsP7ULg41iY3MP6FX
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Carve the motivic resolution layer out of the integration branch as the next tranche after the algebra engine (SpectralSequences#266, merged). Adds CTauAlgebra, the A_C/tau view the ordinary resolution engine resolves, and MotivicResolution: resolve the trivial module over A_C/tau, then lift the differential to A_C by correcting along the weight grading. Includes the resolution cache and the resolve_motivic_ctau example. A_C/tau is F_2[xi_i] tensor E(tau_i) — the odd-primary dual's shape with 2^i for p^i — so its product is the classical one at p = 2: the exterior commutation shifts by 2^k and the signs collapse over F_2. It therefore multiplies through `milnor_product` from the parent commit rather than reimplementing the walk, and a test cross-checks that against the engine's independent closed-form product, which comes from Kong-Lin duality instead. Note that `milnor_product` takes its left factor first while the engine's `product_indexed` orders its arguments the other way; the two agree exactly under that transposition. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013ePtYD7Bt4iPeCtmqtqvZE
Parsing and product invariants in CTauAlgebra: - `Q_k` with k >= 32 was shifted into a 32-bit exterior mask: a debug panic, and in release a masked shift that silently produced the wrong monomial. Module descriptors are untrusted input, so reject it instead. - A product term absent from the degree-t basis was skipped. `enum_basis` holds every such monomial, so a miss is a broken invariant, not a term to drop; say so. - Reuse the `PPartAllocation` across basis products rather than allocating one per call. - The decomposition residual check guarded a silently wrong result, so it now holds in release too. In the resolution: - `MOT_MARGIN` below 1 shrank the compute box under the report box, so readers indexed generators the lift never populated. Clamp it. - The tau-power cast wrapped a negative difference to near u32::MAX, which also defeated the `power >= 1` test guard. Fail on it. - Only the (s=0, t=0) generator is seeded with a weight, so a module that is not cyclic on a degree-0 class left generators unweighted and panicked in the verify path far from the cause. Reject such modules up front. Seeding caller-supplied cell weights is left for the follow-up that needs them. The example now uses `trivial_module` and the `CTauResolution` alias instead of rebuilding both. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013ePtYD7Bt4iPeCtmqtqvZE
… sequence Assemble the lifted differential into a trigraded spectral sequence: E_1 = Ext over A_C/tau with d_1 the weight-1 part of delta, and the higher d_r by the tau-Bockstein zig-zag. Inverting tau gives the classical Adams E_2; finite-page deaths are the motivic tau-torsion. Adds classical_ext_rank and the chart_motivic example. The anchor test asserts that inverting tau reproduces the classical Adams E_2 over the tested range. deformation_products is deferred to the products tranche, since it reads multiplication off the Ext DGA. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013ePtYD7Bt4iPeCtmqtqvZE
The top of the motivic stack: take cohomology of delta to get the motivic Adams E_2, and read products and Massey products off it. - cohomology: the Ext DGA carrying delta as its differential (TauModule, classical_ext_rank), plus f2tau, the dense F_2[tau] linear algebra that reads E_2 as an F_2[tau]-module (invariant factors for tau-torsion, coset reduction for Massey indeterminacy). - products: the product lift and deformation_products. - massey: motivic Massey products with tau, via the null-homotopy lift. Includes the ext_algebra differential/cohomology support from SpectralSequences#267, which this builds on and which is not yet merged; that part drops out of the diff once SpectralSequences#267 lands. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013ePtYD7Bt4iPeCtmqtqvZE
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Draft — top of the motivic stack. Cumulative: contains every tranche below it, so review only the top commit until those land.
What this is
Take cohomology of δ to get the motivic Adams$E_2$ , and read products and Massey products off it.
cohomology— the Ext DGA carrying δ as its differential (MotivicCoboundary),TauModule,classical_ext_rank. This is where thef2tau— dense linear algebra over the PIDu128bitmasks. Readsproducts— the product lift, anddeformation_products.massey— motivic Massey products with τ, via the null-homotopy lift, with indeterminacy as anStack
Depends on #267 (the Ext DGA carrying a differential and computing cohomology), which is not yet merged, so its changes to
ext_algebraandresolution_homomorphismare included here. That part drops out of this diff once #267 lands — it is unmodified from that branch.Also contains the resolution and deformation tranches below it.
Status
Build/clippy/fmt clean. All 19 motivic tests pass, including the hidden τ-extension, Massey products with τ, and τ-module torsion agreeing with the deformation SS sources. The 10
ext_algebratests from #267 pass unchanged on current master.Generated by Claude Code